An introduction to backward SDEs and applications in finance and economics

Abstract:

Backward stochastic differential equations (BSDEs for short) have been introduced since the 90s, and have proved since then to be a fundamental tool in stochastic analysis, stochastic control, and even PDE analysis, with numerous applications in finance, economics and insurance. This course would be the occasion to provide an introduction to the theory as well as its latest developments. After going through some of the most important theoretical results, we will see as an illuminating application how BSDEs allow to treat in a general fashion several problems stemming from contract theory with moral hazard.